Sound intensity is the time-average flow of sound power, per unit area, in the direction of sound propagation. It is generally measured in watts per square meter using the cross-spectral relation, which is the imaginary part of the cross spectrum of the sound pressure between a pair of closely-spaced microphones. This relation was discovered by                1. J. Y. Chung, “Cross-spectral method of measuring acoustic intensity without error caused by instrument phase mismatch”, Journal of the Acoustical Society of America, Vol. 64, NO. 4, pp 1613-1616, (1978).It is based on finite-element approximations that are valid when the spacing between a pair of microphones is less than the wavelength being measured, divided by 2π. The pair of microphones can either be in the side-by-side or face-to-face arrangement with the direction of the measurement along the line joining the geometric centers of the microphone faces. The measurement point is midway between the microphones.        
In prior art, the probes are mainly of two types. One type consists of two microphones in the face-to-face arrangement. The other type consists of a single miniature microphone and two hot-wire anemometers. The present invention has three miniature microphones in a geometric straight line, in the side-by-side arrangement.
In the first type of probe in prior art, with two microphones in the face-to-face arrangement, the microphones are held together by a U-shaped structure. Generally the microphones are larger (diam. typically 12.7 mm) than in the present invention (diam. about 2.6 mm). Examples of such two-microphone probes are:                2. Sound Intensity Probe Kit—Page 31, Product Catalog, Bruel & Kjaer, Headquartered at DK-2850, Naerum, Denmark (2011).        3. Intensity Probes—Page 15, Product Catalog, GRAS, Headquartered at Skovlytoften 33, 2840 Holte, Denmark (2011).Different sizes of spacers between the two microphones are used to cover different frequency ranges in the measurement. Compared to the invention, this type of probe appears to have four possible drawbacks: (a) the U-shaped structure supporting the microphones prevents the probe from being held close to a vibrating surface; (b) it can be difficult to align the probe perpendicularly to a vibrating surface; (c) the position of the measurement point on the vibrating surface may not be accurately determined; and (d) the spacers have to be changed by hand.        
Both the face-to-face and side-by-side arrangements of the microphones have to meet two conditions for the microphone spacing. First, as indicated by J. Y. Chung in reference 1 above, the cross-spectral relation requires the spacing to be less than the wavelength being measured, divided by 2π. When this condition is not met, measurement error can result, as shown in                4. M. J. Crocker and F. Jacobsen, “Sound Intensity”, FIG. 7, Page 1862 Chapter 156, Volume 4, of “Encyclopedia of Acoustics” edited by M. J. Crocker, (John Wiley & Sons, New York, 1997).Measurement error also results when there is phase mismatch between the microphones. This can be avoided or reduced, either by matching microphones, or by using a correction technique developed by J. Y. Chung in reference 1, based on switching the positions of the microphones.        
The second type of probe in prior art has a single microphone that measures sound pressure combined with two hot-wire anemometers that measure sound particle velocity. Sound intensity is the product of the two measurements. Usually the purpose of a hot-wire anemometer is to measure gas flow. This second type of probe is manufactured by Microflown Technologies, headquarted at Zevenaar, Holland, and is described, for example, in                5. Sound-Intensity Probe, Slide 6 of salesperson's power-point description of the Microflown probe, (2011).A possible drawback with this type of probe is the interference with the hot-wire measurements that can occur when there are stray gas currents near operating machinery, or from wind gusts in the open. Another possible drawback is that an extension of the geometric straight line between the hot wires may not accurately determine the measurement point on a vibrating surface.        
In the three-microphone probe of the present invention, the microphones can be matched and calibrated using the method described in                6. R. Hickling, “Normalization and Calibration of Microphones in Sound-Intensity Probes”, U.S. Pat. No. 7,526,094, Apr. 28, (2009).The matching and calibration are performed, using transfer functions, over the entire frequency range of the sound-intensity measurement. In prior art, it is often assumed that the microphone response is substantially uniform and hence that calibration need only be performed at a single frequency. Additionally, in the three-microphone probe of the present invention, the geometric line formed by the three microphones can be extended to accurately determine the position of the measurement point on the vibrating surface.        
Finally, there is another method in prior art in which sound intensity is determined using an array of microphones near a vibrating surface. Sound intensity at the vibrating surface is calculated from sound pressure measured by the microphones in the array, using a mathematical procedure called nearfield acoustical holography (NAH), described in                7. J. D. Maynard, E. G. Williams and Y. Lee, “Nearfield acoustic holography. I. Theory of generalized holography and the development of NAH”. Journal of the Acoustical Society of America, Vol. 78, No. 4, pp 1395-1413, (1985).The drawbacks of this method are: (a) the difficulty of positioning an array of microphones near a complex vibrating surface and (b) possible error due to the approximations in the NAH calculations. Also the spacing of the microphones in the array may not accurately locate the peaks and valleys of the sound intensity at the vibrating surface.        